Bond order wave (BOW) phase of the extended Hubbard model: Electronic solitons, paramagnetism, coupling to Peierls and Holstein phonons

The bond order wave (BOW) phase of the extended Hubbard model (EHM) in one dimension (1D) is characterized at intermediate correlation $U = 4t$ by exact treatment of $N$-site systems. Linear coupling to lattice (Peierls) phonons and molecular (Holstein) vibrations are treated in the adiabatic approximation. The molar magnetic susceptibility $chi_M(T)$ is obtained directly up to $N = 10$. The goal is to find the consequences of a doubly degenerate ground state (gs) and finite magnetic gap $E_m$ in a regular array. Degenerate gs with broken inversion symmetry are constructed for finite $N$ for a range of $V$ near the charge density wave (CDW) boundary at $V approx 2.18t$ where $E_m approx 0.5t$ is large. The electronic amplitude $B(V)$ of the BOW in the regular array is shown to mimic a tight-binding band with small effective dimerization $delta_{eff}$. Electronic spin and charge solitons are elementary excitations of the BOW phase and also resemble topological solitons with small $delta_{eff}$. Strong infrared intensity of coupled molecular vibrations in dimerized 1D systems is shown to extend to the regular BOW phase, while its temperature dependence is related to spin solitons. The Peierls instability to dimerization has novel aspects for degenerate gs and substantial $E_m$ that suppresses thermal excitations. Finite $E_m$ implies exponentially small $chi_M(T)$ at low temperature followed by an almost linear increase with $T$. The EHM with $U = 4t$ is representative of intermediate correlations in quasi-1D systems such as conjugated polymers or organic ion-radical and charge-transfer salts. The vibronic and thermal properties of correlated models with BOW phases are needed to identify possible physical realizations.